matlab毕业编程【谷速软件】多变量函数的最速下降法.doc

%Steepest Descent Method for Multiple Variable Functionsclc;close all;clear all;format long;disp(Steepest Descent Method);disp(=);%Starting pointsx01=-1;x02=0;%Function F in Symbolic Formata=-(3*x1+x2+6*x1*x2-2*(x12)+2*(x22);%Insert the desired magnitude of final direction vector (0.0001 is fine)eserror=0.0001;%Leave the rest unchanged%=syms x1 x2% Hessian Of Fdisp( sprintf(Function = %s, a);A=diff(diff(a,x1),x1),diff(diff(a,x1),x2);. diff(diff(a,x2),x1),diff(diff(a,x2),x2);%First Order Derivative of FB=diff(a,x1);diff(a,x2);disp Hessian.;pretty(simplify(A)disp Gradient.;pretty(simplify(B)disp(Eigen Values);v,d=eig(A);disp(d);num_of_iterations=1;syms alphaf=(subs(subs(a,x1,x01),x2,x02); disp(sprintf(f(x0)=%f,f);while (num_of_iterations7) disp(_); disp(sprintf(Iteration = %d, num_of_iterations); temp=(subs(subs(B,x1,x01),x2,x02); disp(sprintf(Gradient of X%d, num_of_iterations-1); disp(temp); temp4=(x01;x02); disp(sprintf(X%d =, num_of_iterations-1); disp(temp4); temp = temp4-alpha.*(temp); disp(sprintf(X%d - alpha. gradient(X%d) =, num_of_iterations-1, num_of_iterations-1); disp(temp); f_alpha= subs(subs(a,x1, temp(1,1), x2, temp(2,1); disp(sprintf(f(X%d - alpha. gradient(X%d) =, num_of_iterations-1, num_of_iterations-1); disp(f_alpha); diff_f_alpha = diff(f_alpha,alpha); disp(sprintf(diff(f(X%d - alpha. gradient(X%d)/diff alpha =, num_of_iterations-1, num_of_iterations-1); disp(diff_f_alpha); alphaval=solve(diff_f_alpha, alpha) alphaval2=eval(alphaval) if alphaval20 disp Diverges; break; end newxkplus1 = x01;x02-alphaval2.*(subs(subs(B,x1,x01),x2,x02); x01 = newxkplus1(1,1); x02 = newxkplus1(2,1); disp(sprintf(x%d =,num_of_iterations); disp(newxkplus1) num_of_iterations=num_of_ite